SAT Algebra

Mastering SAT Algebra :  Part 1

  • The quiz consists of 200 questions, and the user will be presented with a unique set of 10 questions in each session for a diverse experience
  • Please note that answers cannot be deselected once chosen in the quiz, so make your choices carefully for an optimal testing experience.
  • Each question is meticulously crafted to mirror the complexity and diversity of  problem-solving you'll encounter in the SAT.
  • Use it as a targeted practice tool to identify and address specific areas of improvement.
  • Track your progress and see your proficiency grow.
1. 

Which of the following expressions is equivalent
to a(b - c)-b(a + c)-c(a - b)

2. 

The graph of the inequality y ≤ 2x will include all of the points in
which quadrant?

3. 

In the system of linear equations below, k is a constant. If the system
has no solution, what is the value of k?
$$(k-1)x+\frac{1}{3}y=4$$
$$k(x+2y)=7$$

4. 

For the system of equations below, which of the following statements
is true?
3x + 5 = 2y
\(\frac{x}{3}+\frac{y}{2}=\frac{2}{3}\)

5. 

Which of the following equations represents a line in the xy-coordinate plane with a
y-intercept of 6 and a slope of − 3?

6. 

In 2014, the United States Postal Service charged €0.48 to mail a first-class letter weighing up to 1 oz. and €0.21 for each additional ounce.
Based on these rates, which function would determine the cost, in
dollars, c(z), of mailing a first-class letter weighing z ounces where z is
an integer greater than 1?

7. 

Which of the following is an equation of a line that is parallel to the
line (1/2 )y - (2/3)x = 6in the xy-plane?

8. 

If point E(5, h) is on the line that contains A(0, 1) and B(−2, −1), what
is the value of h?

9. 

Which of the following equations has a slope perpendicular to the slope of a line with the equation y = ax + b, given that a and b are constants?

10. 

If function f is defined by f(x) = 5x + 3, then which expression
represents 2f(x) – 3?

11. 

In 2012, a retail chain of fast food restaurants had 68 restaurants in
California and started to expand nationally by adding 9 new restaurants
each year thereafter. At this rate, which of the following functions f
represent the number of restaurants there will be in this retail chain n
years after 2012 assuming none of these restaurants close?

12. 

A function f is defined such that f(1) = 2, f(2) = 5, and f(n) = f(n − 1) − f(n − 2) for all integer values of n greater than 2. What is the value of f(4)?

13. 

Let h be the function defined by h(x) = x + 4x. What is the value of 
$$h(\frac{-1}{2})$$

14. 

Which of the following is equivalent to the expression below?
x²− 8x + 5

15. 

What is the slope of a line with the equation 5x + 4y = 2?

16. 

The net profit for the sales of a product is equal to
the total revenue from the sales of that product
minus the total cost for the sales of that product. If a
particular model of calculator sells for €98, and the
cost for making and selling n of these calculators is
€(35n + 120,000), which of the following equations
expresses the net profit in dollars, P, for making and
selling n of these calculators?

17. 

If the function f is defined by f(x) = 3x + 2, and if f(a) = 17, what is the
value of a?

18. 

For the equation 1/2 y= 2/3 x -4, what is the x-intercept?

19. 

The equation a + b = 15 relates the number of hours, a, Kevin
spends doing homework each week and the number of hours he
spends watching television each week. If Kevin spends a total of
15 hours doing homework and watching television each week,
what does the variable b represent?

20. 

If  \(a=60(99)^{99}+ 30(99)^{99}, b=99^{100},c=90(90)^{99}\)
then which of the following expresses the correct
ordering of a, b, and c

21. 

Which of the following expressions is NOT
equivalent to p - 2/3 (2p - 3q) - 1/3 (p + 4q)

22. 

Which ordered pair (x, y) satisfies the system of equations
shown below?
3x - (y/3) = 21
x = y+7

23. 

For what value of k does the system of equations below have no
solution?
4x + 6y = 12
y = 8 − kx

24. 

(4 − a²) − (2a² − 6)
Which of the following expressions is equivalent to the one
above?

25. 

In a certain greenhouse for plants, the Fahrenheit temperature, F, is
controlled so that it does not vary from 79° by more than 7°. Which of
the following best expresses the possible range in Fahrenheit
temperatures of the greenhouse?

26. 

If \(\frac{|a+3|}{2}\) =1 and 2|b + 1| = 6, then |a + b| could equal any of the
following EXCEPT

27. 

According to market research, the number of magazine subscriptions
that can be sold can be estimated using the function
$$n(p)=\frac{5,000}{4p-k}$$
where n is the number of thousands of subscriptions sold, p is the price
in euros for each individual subscription, and k is some constant. If
250,000 subscriptions were sold at €15 for each subscription, how
many subscriptions could be sold if the price were set at €20 for each
subscription?

28. 

If 2 times an integer x is increased by 5, the result is always greater than 16 and less than 29. What is the least value of x?

29. 

Which of the following expressions is NOT
equivalent to 3 [6a-3(1 - a) - 5(a + 1)

30. 

The line y + 2x = b is perpendicular to a line that passes through the
origin. If the two lines intersect at the point (k + 2, 2k), what is the
value of k?

31. 

If the below system of equations has infinitely many solutions, what is
the value of  p/q?
6x+py = 21
qx+5y=7

32. 

Which of the following expressions is equivalent to
2/4(a²-a-3) + 1/3 (a²+2a+6)

33. 

The ninth grade class at a local high school needs to purchase a park permit for €250.00 for their upcoming class picnic. Each ninth grader attending the picnic pays €0.75. Each guest pays €1.25. If 200 ninth graders attend the picnic, which inequality can be used to determine the number of guests, x, needed to cover the cost of the permit?

34. 

For the inequality below, what is a possible value of x-3?
$$-\frac{5}{3}< \frac{1}{2}-\frac{1}{3}x<\frac{-3}{2}$$

35. 

The graph of a line in the xy-plane has slope and contains the point
(0, 7). The graph of a second line passes through the points (0, 0) and
(–1, 3). If the two lines intersect at the point (r, s), what is the value of
r + s?

36. 

Which could be the slope of a line that contains (1, 1) and passes
between the points (0, 2) and (0, 3)?

37. 

Roger is having a picnic for 78 guests. He plans to serve each guest at least one hot dog. If each package, p, contains eight hot dogs, which inequality could be used to determine the number of packages of hot dogs Roger must buy?

38. 

The point whose coordinates are (4, −2) lies on a line whose slope is .
Which of the following are the coordinates of another point on this
line?

39. 

what is the value of
$$\frac{7\div (q)^{2}\times 2}{2p}\times \frac{-p+6q-r}{-q}$$
if p =4, q= 1/2 and r = 2?

40. 

Segments AP and BP have the same length. If the coordinates of A and
P are (−1, 0) and (4, 12), respectively, which could be the coordinates
of B?
I. \((\frac{3}{2},6)\)
II (9,24)
III(-8,7)

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